Some fixed point theorems on non-convex sets

M. Radhakrishnan

India

University of Madras

Ramanujan Institute for Advanced Study in Mathematics

S. Rajesh

India

Indian Institute of Technology

Department of Mathematics

Sushama Agrawal

India

University of Madras

Ramanujan Institute for Advanced Study in Mathematics
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Accepted: 2017-06-08

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Published: 2017-10-02

DOI: https://doi.org/10.4995/agt.2017.7452
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Keywords:

fixed points, nonexpansive mappings, T-regular set, k-uniform convex Banach spaces, Opial property

Supporting agencies:

This research was not funded

Abstract:

In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$
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